Question

Sales. Suppose a bicycle company projects sales to increase with the function $f(x) = 3(x + 3)^2$ Using the definition of the derivative, $f'(x)$ is equal to $\frac{6h + 3h^2 + 3hx}{h}$ $\frac{18h + 3h^2 + 6hx}{h}$ $\frac{18h + 3h^2}{h}$ $\lim_{h \to 0} 18h + 3h^2 + 6hx$ None of the other answers $\lim_{h \to 0} \frac{18h + 3h^2 + 6hx}{h}$ $\lim_{h \to 0} \frac{6h + 3h^2 + 3hx}{h}$ $\lim_{h \to 0} \frac{18h + 3h^2}{h}$

          Sales. Suppose a bicycle company projects sales to increase with the function $f(x) = 3(x + 3)^2$
Using the definition of the derivative, $f'(x)$ is equal to
$\frac{6h + 3h^2 + 3hx}{h}$
$\frac{18h + 3h^2 + 6hx}{h}$
$\frac{18h + 3h^2}{h}$
$\lim_{h \to 0} 18h + 3h^2 + 6hx$
None of the other answers
$\lim_{h \to 0} \frac{18h + 3h^2 + 6hx}{h}$
$\lim_{h \to 0} \frac{6h + 3h^2 + 3hx}{h}$
$\lim_{h \to 0} \frac{18h + 3h^2}{h}$

Sales. Suppose a bicycle company projects sales to increase with the function f(x) = 3(x + 3)^2
Using the definition of the derivative, f'(x) is equal to
(6h + 3h^2 + 3hx)/(h)
(18h + 3h^2 + 6hx)/(h)
(18h + 3h^2)/(h)
limh → 0 18h + 3h^2 + 6hx
None of the other answers
limh → 0(18h + 3h^2 + 6hx)/(h)
limh → 0(6h + 3h^2 + 3hx)/(h)
limh → 0(18h + 3h^2)/(h)

Added by Renee W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Keerti J

Step 1

The power rule states that if we have a function of the form f(x) = ax^n, then the derivative is given by f'(x) = nax^(n-1). In this case, we have f(x) = 3(x^2 + 3)^2. To find the derivative, we need to apply the power rule twice. First, we differentiate the Show more…

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Sales. Suppose the bicycle company projects sales to increase with the function f(x) = 3(x^2 + 3)^2. Using the definition of the derivative, f'(x) is equal to: 6x + 3(2x)(x^2 + 3) 18x + 6x^3 + 9x 18x + 6x^3 + 9x Iim 18x + 6x^3 - 9x None of the other answers 18x + 6x^3 + 9x Iim 3(2x)(x^2 + 3) Iim h->0 18x + 6x^3 Iim h->0